I must take a more detailed look at those links but in the meantime I hope the below is useful as a quick summary of loco-hauled stock in the diesel era. Experts will no doubt point out various over-simplifications and exceptions!
With freight the main issue is compatibility of brakes. Any British wagon since the 70s will have a TOPS data panel with a three-letter code on the top row. The last letter indicates brake type. A is air brake, V is vacuum and O is no continuous brake fitted. All wagons have hand brakes. There are other codes to allow for dual fitting and wagons fitted with a through pipe but no continuous brake. The code is usually quite easy to pick out on photos.
BR standardised on air brakes in the mid-60s so any new wagon after that date would be air braked. Some older wagons were retro-fitted with air brakes too.
The old unfitted freight trains ran until the 1980s and a variant was the partly fitted freight train where the wagons at the front of the train were vacuum fitted and connected up to the loco to provide additional brake force. Either type of train required a brake van at the rear, with the guard assisting in control of the train and importantly also responsible for safely stopping it a coupling broke somewhere in the train. Incidentally wagons with either type of continous brake could run in unfitted trains with the continous brakes not operating. Vacuum-fitted freight trains continued in diminishing numbers, particularly on engineers trains, but are now pretty much extinct.
With passenger trains there is a similar issue with brakes. Passenger trains must be fully fitted with continuous brakes so the loco and all the stock must have the same braking system. Also, unlike wagons, only "brake" coaches have a handbrake so every train would have to include at least one brake coach so it could be secured properly if the locomotive was removed (leaks in the on-board equipment make the continuous brake ineffective after a few hours if not connected to a locomotive). Mk1 and early Mk2 stock were vacuum braked but many of these (especially buffets and brake or parcels vans) were dual fitted or converted to air braking as the later builds did not include enough of these types.
With passenger trains there is also the question of heating. Mk1 and early Mk2 stock was fitted with steam heating and some also with electric train heating (ETH). The later Mk2 stock, including all the air conditioned versions, had only ETH. High Speed Trains use their own system which is incompatible with the apparently similar loco-hauled Mk3 coaches. Normal practice was for the loco and all coaches to be fitted with the same heating system but exceptions did occur in emergencies and in summer it was common for non-air-conditioned stock to be hauled by locos with no heating equipment (particularly on seaside excursions!).
The types of coach fitted from new with ETH or air brakes are relatively easy to distinguish in photographs, particularly the air-conditioned types, but retrofits are harder to spot unless they are in a train with an obviously ETH or air-braked vehicle. A "spotter book" of coaching stock for your period will give full details for each vehicle.
What does this mean for locomotives? All diesels built up until the mid-60s were delivered with vacuum brakes and for classes intended for passenger use some at least were fitted with steam heat boilers. From the mid-60s onwards new passenger classes had electric train heating generators and no steam boilers.
Many older locos were also retro-fitted with ETH and these were renumbered into separate sub-classes when the five-digit TOPS numbering system came in. Thus class 47s above 47401 were ETH fitted, all class 31s above 31401 but for class 37 only the few numbered 374xx. To answer your specific query only this 374xx sub-class can haul Mk3 coaches though it wouldn't have enough power to heat a full length train (or probably even haul it at a reasonable speed). Some classes never had ETH equipment, including those such as Class 40 which were originally seen as passenger locos but were increasingly relegated to freight duties. At the same time steam heat boilers were removed, isolated, or left operational on an apparently random basis. ETH can be discerned from photographs either from the number series or by looking for the heating connections which are coloured orange and located outboard of each buffer. With steam heating it is possible to tell if the visible parts of the equipment are missing but not if they are still present but no longer working. Otherwise you will need to get hold of a stock book for your period of interest.
The situation with brakes is quite similar. New types from the early 70s onwards (Class 56) only had air brakes. Many of the vacuum-only types were retrofitted with air brakes but the vacuum systems were left in place. If a loco had ETH is it safe to assume that is also had air brakes, since virtually all ETH stock was air braked. In the case of non-ETH locos the fitment of air brakes was pretty random, and again you need to locate a stock book unless you can see the buffer beam air pipes in a picture of the loco in question. These are red and yellow tipped but difficult to distinguish when dirty and particularly in a black and white photo!
As the older classes were withdrawn from the 70s onwards non-ETH and particularly vacuum-only locomotives would be obvious candidates to go first.
With freight the main issue is compatibility of brakes. Any British wagon since the 70s will have a TOPS data panel with a three-letter code on the top row. The last letter indicates brake type. A is air brake, V is vacuum and O is no continuous brake fitted. All wagons have hand brakes. There are other codes to allow for dual fitting and wagons fitted with a through pipe but no continuous brake. The code is usually quite easy to pick out on photos.
BR standardised on air brakes in the mid-60s so any new wagon after that date would be air braked. Some older wagons were retro-fitted with air brakes too.
The old unfitted freight trains ran until the 1980s and a variant was the partly fitted freight train where the wagons at the front of the train were vacuum fitted and connected up to the loco to provide additional brake force. Either type of train required a brake van at the rear, with the guard assisting in control of the train and importantly also responsible for safely stopping it a coupling broke somewhere in the train. Incidentally wagons with either type of continous brake could run in unfitted trains with the continous brakes not operating. Vacuum-fitted freight trains continued in diminishing numbers, particularly on engineers trains, but are now pretty much extinct.
With passenger trains there is a similar issue with brakes. Passenger trains must be fully fitted with continuous brakes so the loco and all the stock must have the same braking system. Also, unlike wagons, only "brake" coaches have a handbrake so every train would have to include at least one brake coach so it could be secured properly if the locomotive was removed (leaks in the on-board equipment make the continuous brake ineffective after a few hours if not connected to a locomotive). Mk1 and early Mk2 stock were vacuum braked but many of these (especially buffets and brake or parcels vans) were dual fitted or converted to air braking as the later builds did not include enough of these types.
With passenger trains there is also the question of heating. Mk1 and early Mk2 stock was fitted with steam heating and some also with electric train heating (ETH). The later Mk2 stock, including all the air conditioned versions, had only ETH. High Speed Trains use their own system which is incompatible with the apparently similar loco-hauled Mk3 coaches. Normal practice was for the loco and all coaches to be fitted with the same heating system but exceptions did occur in emergencies and in summer it was common for non-air-conditioned stock to be hauled by locos with no heating equipment (particularly on seaside excursions!).
The types of coach fitted from new with ETH or air brakes are relatively easy to distinguish in photographs, particularly the air-conditioned types, but retrofits are harder to spot unless they are in a train with an obviously ETH or air-braked vehicle. A "spotter book" of coaching stock for your period will give full details for each vehicle.
What does this mean for locomotives? All diesels built up until the mid-60s were delivered with vacuum brakes and for classes intended for passenger use some at least were fitted with steam heat boilers. From the mid-60s onwards new passenger classes had electric train heating generators and no steam boilers.
Many older locos were also retro-fitted with ETH and these were renumbered into separate sub-classes when the five-digit TOPS numbering system came in. Thus class 47s above 47401 were ETH fitted, all class 31s above 31401 but for class 37 only the few numbered 374xx. To answer your specific query only this 374xx sub-class can haul Mk3 coaches though it wouldn't have enough power to heat a full length train (or probably even haul it at a reasonable speed). Some classes never had ETH equipment, including those such as Class 40 which were originally seen as passenger locos but were increasingly relegated to freight duties. At the same time steam heat boilers were removed, isolated, or left operational on an apparently random basis. ETH can be discerned from photographs either from the number series or by looking for the heating connections which are coloured orange and located outboard of each buffer. With steam heating it is possible to tell if the visible parts of the equipment are missing but not if they are still present but no longer working. Otherwise you will need to get hold of a stock book for your period of interest.
The situation with brakes is quite similar. New types from the early 70s onwards (Class 56) only had air brakes. Many of the vacuum-only types were retrofitted with air brakes but the vacuum systems were left in place. If a loco had ETH is it safe to assume that is also had air brakes, since virtually all ETH stock was air braked. In the case of non-ETH locos the fitment of air brakes was pretty random, and again you need to locate a stock book unless you can see the buffer beam air pipes in a picture of the loco in question. These are red and yellow tipped but difficult to distinguish when dirty and particularly in a black and white photo!
As the older classes were withdrawn from the 70s onwards non-ETH and particularly vacuum-only locomotives would be obvious candidates to go first.
